Stability for the complete intersection theorem, and the forbidden intersection problem of Erd?os and Sós.

A family F of sets is said to be t -intersecting if for any A; B 2 F . The seminal Complete Intersection Theorem of Ahlswede and Khachatrian (1997) gives the maximal size f .n; k; t of a t -intersecting family of k-element subsets of OEn D together with a characterisation of the extremal families, solving a longstanding problem of Frankl. The forbidden intersection problem, posed by Erdos and Sós in 1971, asks for a determination of the maximal size g.n; k; t / of a family F of k-element subsets of OEn such that jA \ Bj ¤ for any A, B F. [ABSTRACT FROM AUTHOR]